Homogenization of elliptic systems with periodic coefficients: operator error estimates in L_2(R^d) with corrector taken into account

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Homogenization of elliptic systems with periodic coefficients: operator error estimates in L_2(R^d) with corrector taken into account. / Suslina, T. A.

In: St. Petersburg Mathematical Journal, Vol. 26, No. 4, 2015, p. 643-693.

Research output: Contribution to journal › Article › peer-review

BibTeX

@article{085dbff550b441b49fd9cd217837cf59,

title = "Homogenization of elliptic systems with periodic coefficients: operator error estimates in L_2(R^d) with corrector taken into account",

abstract = "{\textcopyright} 2015 American Mathematical Society.A matrix elliptic selfadjoint second order differential operator (DO) Bε with rapidly oscillating coefficients is considered in L2(Rd;Cn). The principal part b(D)*g(ε-1x)b(D) of this operator is given in a factorized form, where g is a periodic, bounded, and positive definite matrix-valued function and b(D) is a matrix first order DO whose symbol is a matrix of maximal rank. The operator Bε also includes first and zero order terms with unbounded coefficients. The problem of homogenization in the small period limit is studied. For the generalized resolvent of Bε, approximation in the L2(Rd;Cn)-operator norm with an error O(ε2) is obtained. The principal term of this approximation is given by the generalized resolvent of the effective operator B0 with constant coefficients. The first order corrector is taken into account. The error estimate obta",

author = "Suslina, {T. A.}",

year = "2015",

doi = "10.1090/spmj/1354",

language = "English",

volume = "26",

pages = "643--693",

journal = "St. Petersburg Mathematical Journal",

issn = "1061-0022",

publisher = "American Mathematical Society",

number = "4",

}

RIS

TY - JOUR

T1 - Homogenization of elliptic systems with periodic coefficients: operator error estimates in L_2(R^d) with corrector taken into account

AU - Suslina, T. A.

PY - 2015

Y1 - 2015

N2 - © 2015 American Mathematical Society.A matrix elliptic selfadjoint second order differential operator (DO) Bε with rapidly oscillating coefficients is considered in L2(Rd;Cn). The principal part b(D)*g(ε-1x)b(D) of this operator is given in a factorized form, where g is a periodic, bounded, and positive definite matrix-valued function and b(D) is a matrix first order DO whose symbol is a matrix of maximal rank. The operator Bε also includes first and zero order terms with unbounded coefficients. The problem of homogenization in the small period limit is studied. For the generalized resolvent of Bε, approximation in the L2(Rd;Cn)-operator norm with an error O(ε2) is obtained. The principal term of this approximation is given by the generalized resolvent of the effective operator B0 with constant coefficients. The first order corrector is taken into account. The error estimate obta

AB - © 2015 American Mathematical Society.A matrix elliptic selfadjoint second order differential operator (DO) Bε with rapidly oscillating coefficients is considered in L2(Rd;Cn). The principal part b(D)*g(ε-1x)b(D) of this operator is given in a factorized form, where g is a periodic, bounded, and positive definite matrix-valued function and b(D) is a matrix first order DO whose symbol is a matrix of maximal rank. The operator Bε also includes first and zero order terms with unbounded coefficients. The problem of homogenization in the small period limit is studied. For the generalized resolvent of Bε, approximation in the L2(Rd;Cn)-operator norm with an error O(ε2) is obtained. The principal term of this approximation is given by the generalized resolvent of the effective operator B0 with constant coefficients. The first order corrector is taken into account. The error estimate obta

U2 - 10.1090/spmj/1354

DO - 10.1090/spmj/1354

M3 - Article

VL - 26

SP - 643

EP - 693

JO - St. Petersburg Mathematical Journal

JF - St. Petersburg Mathematical Journal

SN - 1061-0022

IS - 4

ER -

ID: 3976840